# LMS color space

Normalized responsivity spectra of human cone cells, S, M, and L types

LMS is a color space represented by the response of the three types of cones of the human eye, named for their responsivity (sensitivity) peaks at long, medium, and short wavelengths.

It is common to use the LMS color space when performing chromatic adaptation (estimating the appearance of a sample under a different illuminant). It's also useful in the study of color blindness, when one or more cone types are defective.

## XYZ to LMS

Typically, colors to be adapted chromatically will be specified in a color space other than LMS. The chromatic adaptation matrix in the von Kries transform method, however, expects the LMS color space. The relationship between the XYZ and LMS color spaces is linear, so the transition is representable by a transformation matrix.

Since the LMS color space is supposed to model the complex human color perception, no single, “objective” transformation matrix between XYZ and LMS exists[dubious ]. Instead, various Color Appearance Models (CAMs) offer various Chromatic Adaptation Transform (CAT) matrices M as part of their modeling of human color perception.

The CAT matrices for some CAMs in terms of CIEXYZ coordinates are presented here.

Notes

### Hunt, RLAB

The Hunt and RLAB color appearance models use the Hunt-Pointer-Estevez transformation matrix (MHPE) for conversion from CIE XYZ to LMS.[1][2] This is the transformation matrix which was originally used in conjunction with the von Kries transform method, and is therefore also called von Kries transformation matrix (MvonKries).

 Equal-energy illuminants: ${\displaystyle {\begin{bmatrix}L\\M\\S\end{bmatrix}}={\begin{bmatrix}0.38971&0.68898&-0.07868\\-0.22981&1.18340&0.04641\\0.00000&0.00000&1.00000\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}}$ Normalized to D65: ${\displaystyle {\begin{bmatrix}L\\M\\S\end{bmatrix}}={\begin{bmatrix}0.4002&0.7076&-0.0808\\-0.2263&1.1653&0.0457\\0&0&0.9182\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}}$

### CIECAM97s, LLAB

The original CIECAM97s color appearance model uses the Bradford transformation matrix (MBFD) (as does the LLAB color appearance model).[1] This is a “spectrally sharpened” transformation matrix (i.e. the L and M cone response curves are narrower and more distinct from each other). The Bradford transformation matrix was supposed to work in conjunction with a modified von Kries transform method which introduced a small non-linearity in the S (blue) channel. However, outside of CIECAM97s and LLAB this is often neglected and the Bradford transformation matrix is used in conjunction with the linear von Kries transform method, explicitly so in ICC profiles.[3]

${\displaystyle {\begin{bmatrix}L\\M\\S\end{bmatrix}}={\begin{bmatrix}0.8951&0.2664&-0.1614\\-0.7502&1.7135&0.0367\\0.0389&-0.0685&1.0296\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}}$

A revised version of CIECAM97s switches back to a linear transform method and introduces a corresponding transformation matrix (MCAT97s):[4]

${\displaystyle {\begin{bmatrix}L\\M\\S\end{bmatrix}}={\begin{bmatrix}0.8562&0.3372&-0.1934\\-0.8360&1.8327&0.0033\\0.0357&-0.0469&1.0112\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}}$

### CIECAM02

CIECAM02 is the successor to CIECAM97s; its transformation matrix (MCAT02) is:[1]

${\displaystyle {\begin{bmatrix}L\\M\\S\end{bmatrix}}={\begin{bmatrix}0.7328&0.4296&-0.1624\\-0.7036&1.6975&0.0061\\0.0030&0.0136&0.9834\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}}$